Exponential decay for Bernoulli percolation via stochastic comparison

Vortrag von Dr. Hugo Vanneuville

Datum: 10.04.24  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

Bernoulli percolation of parameter p on Z^d is defined by deleting each edge of Z^d with probability 1-p, independently of the other edges. The exponential decay theorem -- proven in the 80's by Menshikov and, independently, by Aizenman and Barsky -- can be stated as follows: If the cardinality of the cluster of 0 is a.s. finite at some parameter p, then it has an exponential moment at every parameter q